Cannot delete phantom edge in my model
I believe that the vertex is hidden. To hide something, you select it and key H. This can easily be done by accidentally hitting H on your way to G (grab/translate). Hiding is useful for working on one part of your mesh while not having to work around or Wireframe through other parts. To un-hide, for lack of a better phrase, key Alt + H.

Once you've un-hidden, key X and select Verticies or perhaps Edges in your case.